CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallian’s text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists.
Part 1: Integers and Equivalence Relations
Ch 0: Preliminaries
Part 2: Groups
Ch 1: Introduction to Groups
Ch 2: Groups
Ch 3: Finite Groups; Subgroups
Ch 4: Cyclic Groups
Ch 5: Permutation Groups
Ch 6: Isomorphisms
Ch 7: Cosets and Lagrange’s Theorem
Ch 8: External Direct Products
Ch 9: Normal Subgroups and Factor Groups
Ch 10: Group Homomorphisms
Ch 11: Fundamental Theorem of Finite Abelian Groups
Part 3: Rings
Ch 12: Introduction to Rings
Ch 13: Integral Domains
Ch 14: Ideals and Factor Rings
Ch 15: Ring Homomorphisms
Ch 16: Polynomial Rings
Ch 17: Factorization of Polynomials
Ch 18: Divisibility in Integral Domains
Part 4: Fields
Ch 19: Vector Spaces
Ch 20: Extension Fields
Ch 21: Algebraic Extensions
Ch 22: Finite Fields
Ch 23: Geometric Constructions
Part 5: Special Topics
Ch 24: Sylow Theorems
Ch 25: Finite Simple Groups
Ch 26: Generators and Relations
Ch 27: Symmetry Groups
Ch 28: Frieze Groups and Crystallographic Groups
Ch 29: Symmetry and Counting
Ch 30: Cayley Digraphs of Groups
Ch 31: Introduction to Algebraic Coding Theory
Ch 32: An Introduction to Galois Theory
Ch 33: Cyclotomic Extensions
